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If you are willing to take a difficult theorem of Moise for granted (which proves equivalence of link isotopy in the smooth (tame) and PL category, in his "Affine Structures in 3 Manifolds VIII"), there is a simpleconcise proof in the book "Knot Theory" by Manturov. Although I'm curious about a proof entirely in the smooth category.

If you are willing to take a difficult theorem of Moise for granted (which proves equivalence of link isotopy in the smooth (tame) and PL category, in his "Affine Structures in 3 Manifolds VIII"), there is a simple proof in the book "Knot Theory" by Manturov. Although I'm curious about a proof entirely in the smooth category.

If you are willing to take a difficult theorem of Moise for granted (which proves equivalence of link isotopy in the smooth (tame) and PL category, in his "Affine Structures in 3 Manifolds VIII"), there is a concise proof in the book "Knot Theory" by Manturov.

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If you are willing to take a difficult theorem of Moise for granted (which proves equivalence of link isotopy in the smooth (tame) and PL category, in his "Affine Structures in 3 Manifolds VIII"), there is a simple proof in the book "Knot Theory" by Manturov. Although I'm curious about a proof entirely in the smooth category.